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<Startup-Code startupcode="plots:-setoptions( 'labels' = ['x', 'y'],\012        'font' = [&quot;Times New Roman&quot;, 12],\012        'thickness' = 2 ):\012\012\012M4_2_3a := module()\012    export Click, Drag, EndDrag;\012    local DoPlot, Extend, pos_fn, vel_fn, start, sec1, sec2, fstart, fsec1, fsec2, pos, vel, deltafn;\012    uses DT = DocumentTools;\012\012    start := undefined;\012\012    # Velocity function constructed via a spline through these points:\012    #     [[-10, 10], [-8, 0], [-5, 0], [-2, 5], [0, 0], [2, -4], [3, -3], [6, -5], [8, -12]]\012    #\012    # Position function constructed by numeric integration of the velocity function\012\012    pos_fn := proc( x )\012        local n;\012\012        if type( x, 'undefined' ) then\012            return x;\012        end if;\012\012        n := ceil( 10*x );\012\012        return pos[n,2] + ( pos[n+1,2] - pos[n,2] ) / ( pos[n+1,1] - pos[n,1] ) * ( x - pos[n,1] );\012    end proc; # pos_fn\012\012    vel_fn := proc( x )\012        local n;\012\012        if type( x, 'undefined' ) then\012            return x;\012        end if;\012\012        n := ceil( 10*x );\012\012        return vel[n,2] + ( vel[n+1,2] - vel[n,2] ) / ( vel[n+1,1] - vel[n,1] ) * ( x - vel[n,1] );\012    end proc; # vel_fn\012\012\012####\012    pos := [[0, 688475/11588], [.1, 60.38318602], [.2, 61.29454897], [.3, 62.14704927], [.4, 62.94102999], [.5, 63.67697142], [.6, 64.35549109], [.7, 64.97734377], [.8, 65.54342142], [.9, 66.05475327], [1.0, 66.51250575], [1.1, 66.91798253], [1.2, 67.27262451], [1.3, 67.57800980], [1.4, 67.83585377], [1.5, 68.04800899], [1.6, 68.21646526], [1.7, 68.34334964], [1.8, 68.43092637], [1.9, 68.48159696], [2.0, 68.49790013], [2.1, 68.48250347], [2.2, 68.43811165], [2.3, 68.36737459], [2.4, 68.27287908], [2.5, 68.15714882], [2.6, 68.02264441], [2.7, 67.87176335], [2.8, 67.70684003], [2.9, 67.53014573], [3.0, 67.34388863], [3.1, 67.15021382], [3.2, 66.95120327], [3.3, 66.74887585], [3.4, 66.54518733], [3.5, 66.34203037], [3.6, 66.14123454], [3.7, 65.94456629], [3.8, 65.75372898], [3.9, 65.57036286], [4.0, 65.39604508], [4.1, 65.23228967], [4.2, 65.08054758], [4.3, 64.94220665], [4.4, 64.81859160], [4.5, 64.71096407], [4.6, 64.62052258], [4.7, 64.54840255], [4.8, 64.49567630], [4.9, 64.46335305], [5.0, 64.45237890], [5.1, 64.46363440], [5.2, 64.49790739], [5.3, 64.55586591], [5.4, 64.63805571], [5.5, 64.74490024], [5.6, 64.87670068], [5.7, 65.03363593], [5.8, 65.21576261], [5.9, 65.42301503], [6.0, 65.65520526], [6.1, 65.91202304], [6.2, 66.19303585], [6.3, 66.49768890], [6.4, 66.82530508], [6.5, 67.17508504], [6.6, 67.54610710], [6.7, 67.93732734], [6.8, 68.34757952], [6.9, 68.77557514], [7.0, 69.21990341], [7.1, 69.67903126], [7.2, 70.15130332], [7.3, 70.63494196], [7.4, 71.12804724], [7.5, 71.62859697], [7.6, 72.13444665], [7.7, 72.64332950], [7.8, 73.15285646], [7.9, 73.66051619], [8.0, 74.16367507], [8.1, 74.65958878], [8.2, 75.14553001], [8.3, 75.61891610], [8.4, 76.07732063], [8.5, 76.51847345], [8.6, 76.94026066], [8.7, 77.34072461], [8.8, 77.71806393], [8.9, 78.07063348], [9.0, 78.39694440], [9.1, 78.69566406], [9.2, 78.96561611], [9.3, 79.20578044], [9.4, 79.41529322], [9.5, 79.59344684], [9.6, 79.73968998], [9.7, 79.85362756], [9.8, 79.93502075], [9.9, 79.98378700], [10., 80.], [10.1, 79.98388897], [10.2, 79.93583068], [10.3, 79.85634145], [10.4, 79.74607645], [10.5, 79.60582967], [10.6, 79.43653393], [10.7, 79.23926090], [10.8, 79.01522108], [10.9, 78.76576378], [11.0, 78.49237717], [11.1, 78.19668824], [11.2, 77.88046282], [11.3, 77.54560557], [11.4, 77.19415998], [11.5, 76.82830838], [11.6, 76.45037192], [11.7, 76.06281061], [11.8, 75.66822326], [11.9, 75.26934755], [12.0, 74.86905995], [12.1, 74.47035247], [12.2, 74.07607607], [12.3, 73.68868408], [12.4, 73.31020891], [12.5, 72.94226202], [12.6, 72.58603396], [12.7, 72.24229431], [12.8, 71.91139174], [12.9, 71.59325398], [13.0, 71.28738782], [13.1, 70.99289632], [13.2, 70.70866811], [13.3, 70.43356668], [13.4, 70.16644759], [13.5, 69.90615846], [13.6, 69.65153897], [13.7, 69.40142088], [13.8, 69.15462801], [13.9, 68.90997624], [14.0, 68.66627354], [14.1, 68.42231991], [14.2, 68.17690746], [14.3, 67.92882032], [14.4, 67.67683472], [14.5, 67.41971894], [14.6, 67.15623335], [14.7, 66.88513035], [14.8, 66.60515444], [14.9, 66.31504216], [15.0, 66.01352213], [15.1, 65.69931504], [15.2, 65.37113365], [15.3, 65.02768276], [15.4, 64.66765927], [15.5, 64.28975212], [15.6, 63.89264233], [15.7, 63.47500300], [15.8, 63.03549926], [15.9, 62.57278833], [16.0, 62.08551950], [16.1, 61.57233729], [16.2, 61.03191632], [16.3, 60.46299617], [16.4, 59.86438454], [16.5, 59.23495727], [16.6, 58.57365835], [16.7, 57.87949988], [16.8, 57.15156208], [16.9, 56.38899332], [17.0, 55.59101010], [17.1, 54.75689704], [17.2, 53.88600690], [17.3, 52.97776058], [17.4, 52.03164708], [17.5, 51.04722356], [17.6, 50.02411529], [17.7, 48.96201570], [17.8, 47.86068631], [17.9, 46.71995681], [18.0, 45.53972500], [18.1, 44.31995681], [18.2, 43.06068631], [18.3, 41.76201570], [18.4, 40.42411529], [18.5, 39.04722356], [18.6, 37.63164708], [18.7, 36.17776058], [18.8, 34.68600690], [18.9, 33.15689704], [19.0, 31.59101010], [19.1, 29.98899332], [19.2, 28.35156208], [19.3, 26.67949988], [19.4, 24.97365835], [19.5, 23.23495727], [19.6, 21.46438454], [19.7, 19.66299617], [19.8, 17.83191632], [19.9, 15.97233729], [20.0, 14.08551950]];\012\012    vel := [[0, 10], [.1, 9.4087432], [.2, 8.8188588], [.3, 8.2317189], [.4, 7.6486960], [.5, 7.0711620], [.6, 6.5004895], [.7, 5.9380507], [.8, 5.3852178], [.9, 4.8433633], [1.0, 4.3138591], [1.1, 3.7980779], [1.2, 3.2973918], [1.3, 2.8131730], [1.4, 2.3467938], [1.5, 1.8996268], [1.6, 1.4730438], [1.7, 1.0684175], [1.8, .6871198], [1.9, .3305232], [2.0, 0.], [2.1, -.30341146], [2.2, -.58000834], [2.3, -.83042164], [2.4, -1.05528243], [2.5, -1.25522172], [2.6, -1.43087055], [2.7, -1.58285998], [2.8, -1.71182102], [2.9, -1.81838471], [3.0, -1.90318209], [3.1, -1.96684419], [3.2, -2.01000208], [3.3, -2.03328674], [3.4, -2.03732924], [3.5, -2.02276061], [3.6, -1.99021190], [3.7, -1.94031411], [3.8, -1.87369831], [3.9, -1.79099552], [4.0, -1.69283678], [4.1, -1.57985312], [4.2, -1.45267558], [4.3, -1.31193521], [4.4, -1.15826303], [4.5, -.99229007], [4.6, -.81464738], [4.7, -.62596599], [4.8, -.42687695], [4.9, -.21801127], [5.0, 0.1000000000e-7], [5.1, .22642719], [5.2, .46014611], [5.3, .69993390], [5.4, .94456773], [5.5, 1.19282480], [5.6, 1.44348221], [5.7, 1.69531719], [5.8, 1.94710685], [5.9, 2.19762841], [6.0, 2.44565898], [6.1, 2.68997576], [6.2, 2.92935588], [6.3, 3.16257655], [6.4, 3.388414883], [6.5, 3.605648090], [6.6, 3.813053293], [6.7, 4.009407706], [6.8, 4.193488434], [6.9, 4.364072699], [7.0, 4.519937607], [7.1, 4.659860382], [7.2, 4.782618137], [7.3, 4.886988057], [7.4, 4.971747326], [7.5, 5.035673068], [7.6, 5.077542496], [7.7, 5.096132716], [7.8, 5.090220942], [7.9, 5.058584307], [8.0, 5.000000000], [8.1, 4.913709397], [8.2, 4.800810839], [8.3, 4.662866888], [8.4, 4.501440110], [8.5, 4.318093070], [8.6, 4.114388333], [8.7, 3.891888462], [8.8, 3.652156023], [8.9, 3.396753581], [9.0, 3.127243700], [9.1, 2.845188945], [9.2, 2.552151882], [9.3, 2.249695072], [9.4, 1.939381084], [9.5, 1.622772480], [9.6, 1.301431826], [9.7, .9769216862], [9.8, .6508046255], [9.9, .3246432084], [10., 0.], [10.1, -.3215914739], [10.2, -.6387138420], [10.3, -.9499787711], [10.4, -1.253997928], [10.5, -1.549382983], [10.6, -1.834745599], [10.7, -2.108697445], [10.8, -2.369850190], [10.9, -2.616815499], [11.0, -2.848205039], [11.1, -3.062630480], [11.2, -3.258703487], [11.3, -3.435035726], [11.4, -3.590238868], [11.5, -3.722924578], [11.6, -3.831704522], [11.7, -3.915190370], [11.8, -3.971993786], [11.9, -4.000726441], [12.0, -4.000000003], [12.1, -3.969359078], [12.2, -3.912080078], [12.3, -3.832372366], [12.4, -3.734445289], [12.5, -3.62250820], [12.6, -3.50077045], [12.7, -3.37344140], [12.8, -3.24473040], [12.9, -3.11884682], [13.0, -3.000000005], [13.1, -2.891710961], [13.2, -2.794747368], [13.3, -2.709188563], [13.4, -2.635113878], [13.5, -2.572602651], [13.6, -2.521734215], [13.7, -2.482587904], [13.8, -2.455243056], [13.9, -2.439779004], [14.0, -2.436275082], [14.1, -2.444810626], [14.2, -2.465464973], [14.3, -2.498317454], [14.4, -2.543447408], [14.5, -2.600934166], [14.6, -2.670857056], [14.7, -2.753295431], [14.8, -2.848328621], [14.9, -2.956035948], [15.0, -3.076496757], [15.1, -3.209790384], [15.2, -3.355996162], [15.3, -3.515193428], [15.4, -3.687461515], [15.5, -3.872879750], [15.6, -4.071527487], [15.7, -4.283484040], [15.8, -4.508828755], [15.9, -4.747640967], [16.0, -4.99999998], [16.1, -5.26585844], [16.2, -5.54466169], [16.3, -5.83572863], [16.4, -6.13837764], [16.5, -6.45192763], [16.6, -6.77569729], [16.7, -7.10900529], [16.8, -7.45117015], [16.9, -7.80151084], [17.0, -8.15934587], [17.1, -8.52399402], [17.2, -8.89477388], [17.3, -9.27100435], [17.4, -9.65200381], [17.5, -10.03709117], [17.6, -10.42558510], [17.7, -10.81680431], [17.8, -11.21006730], [17.9, -11.60469303], [18.0, -12.00000001], [18.1, -12.39530702], [18.2, -12.78993267], [18.3, -13.18319575], [18.4, -13.57441494], [18.5, -13.96290883], [18.6, -14.34799623], [18.7, -14.72899571], [18.8, -15.10522608], [18.9, -15.47600602], [19.0, -15.84065413], [19.1, -16.19848920], [19.2, -16.54882981], [19.3, -16.89099477], [19.4, -17.22430276], [19.5, -17.54807237], [19.6, -17.8616224], [19.7, -18.1642714], [19.8, -18.4553383], [19.9, -18.7341416], [20.0, -19.0000000]];\012####\012\012\012    Click := proc()\012        start := undefined;\012        DoPlot();\012    end proc; # Click\012\012    Drag := proc()\012        local x, delta, t;\012\012        if start = undefined then\012            DT:-Do( start = %Plot3( &quot;startx&quot; ) );\012\012            if start &lt; 1 or start &gt; 19 then\012                start := undefined;\012                return NULL;\012            end if;\012\012            deltafn := unapply( .05 * min( 20 - start, start ) * t, t );\012            fstart := pos_fn( start );\012            sec1 := start;\012            sec2 := start;\012            fsec1 := fstart;\012            fsec2 := fstart;\012\012        else\012            DT:-Do( x = %Plot3( &quot;endx&quot; ) );\012\012            if x &lt; 0 or x &gt; 20 then\012                return NULL;\012            end if;\012\012            delta := deltafn( x );\012            sec1 := start - delta;\012            sec2 := start + delta;\012\012            fsec1 := pos_fn( sec1 );\012            fsec2 := pos_fn( sec2 );\012        end if;\012\012        DoPlot();\012    end proc;# Drag\012\012    EndDrag := proc()\012        start := undefined;\012    end proc; # EndDrag\012\012\012    DoPlot := proc()\012        if start = undefined then\012            DT:-Do( %Plot3 = plots:-display( [\012                    plots:-pointplot( \012                        pos,\012                        'style' = 'line',\012                        'colour' = 'blue' )\012                    ],\012                    'labels' = [&quot;tempo&quot;, &quot;posi\303\247\303\243o&quot;],\012                    'labeldirections' = [&quot;horizontal&quot;, &quot;vertical&quot;],\012                    'view' = [0..20, 10..90],\012                    'title' = &quot;Gr\303\241fico de Posi\303\247\303\243o&quot;\012                     ) );\012\012            DT:-Do( %Plot4 = plots:-display( [\012                    plots:-pointplot( \012                        vel,\012                        'style' = 'line',\012                        'colour' = 'blue' )\012                    ],\012                    'labels' = [&quot;tempo&quot;, &quot;velocidade&quot;],\012                    'labeldirections' = [&quot;horizontal&quot;, &quot;vertical&quot;],\012                    'view' = [0..20, -18..10],\012                    'title' = &quot;Gr\303\241fico de Velocidade&quot; ) );\012\012        else\012            DT:-Do( %Plot3 = plots:-display( [\012                    plots:-pointplot( \012                        pos,\012                        'style' = 'line',\012                        'colour' = 'blue' ),\012                    plots:-pointplot( \012                        [Extend( sec1, fsec1, sec2, fsec2, 1 )],\012                        'style' = 'line',\012                        'colour' = 'magenta' ),\012                    plots:-pointplot( \012                        [[sec1, fsec1], [sec2, fsec2]],\012                        'style' = 'point',\012                        'symbol' = 'solidcircle',\012                        'symbolsize' = 20,\012                        'colour' = &quot;DarkGreen&quot; ),\012                    plots:-pointplot( \012                        [[start, fstart]],\012                        'style' = 'point',\012                        'symbol' = 'solidcircle',\012                        'symbolsize' = 20,\012                        'colour' = 'red' ),\012                    plots:-pointplot( \012                        [[start, 10], [start, 90]],\012                        'style' = 'line',\012                        'colour' = 'grey' )\012                    ],\012                    'labels' = [&quot;tempo&quot;, &quot;posi\303\247\303\243o&quot;],\012                    'labeldirections' = [&quot;horizontal&quot;, &quot;vertical&quot;],\012                    'view' = [0..20, 10..90],\012                    'title' = &quot;Gr\303\241fico de Posi\303\247\303\243o&quot;\012                    )\012                );\012\012            DT:-Do( %Plot4 = plots:-display( [\012                    plots:-pointplot( \012                        vel,\012                        'style' = 'line',\012                        'colour' = 'blue' ),\012                    plots:-pointplot( \012                        [start, `if`( sec1 = sec2, vel_fn( start ), ( fsec2-fsec1 )/( sec2-sec1 ) )],\012                        'style' = 'point',\012                        'symbol' = 'solidcircle',\012                        'symbolsize' = 20,\012                        'colour' = 'red' ),\012                    plots:-pointplot( \012                        [[start, -20], [start, 10]],\012                        'style' = 'line',\012                        'colour' = 'grey' )\012                    ],\012                    'labels' = [&quot;tempo&quot;, &quot;velocidade&quot;],\012                    'labeldirections' = [&quot;horizontal&quot;, &quot;vertical&quot;],\012                    'view' = [0..20, -18..10],\012                    'title' = &quot;Gr\303\241fico de Velocidade&quot; )\012                );\012        end if;\012    end proc; # DoPlot\012\012    Extend := proc( a, fa, b, fb, d )\012        local t, L;\012\012        if a = b then\012            # tangent case\012            L := unapply( fa + vel_fn( a ) * (t-a), t );\012\012        else\012            # secant case\012            L := unapply( fa + (fb-fa) / (b-a) * (t-a), t );\012        end if;\012\012        return [a-d, L(a-d)], [b+d, L(b+d)];\012    end proc; # Extend\012\012end module; # M4_3_2a\012\012\012M4_2_3b := module()\012    export Click, Drag, Init;\012    local x, DoPlot, plts, fns, ttls, pts, pos, vel, acc, jrk, pospts, velpts, accpts, jrkpts, view0;\012    uses DT = DocumentTools;\012\012    # The jerk graph was created via a spline fit through these points:\012    #   [[-10, 0], [-5, 5], [-2, 9], [2, 7], [4, 7], [7, 8], [8, 10], [10, 2]]\012    # The acceleration, velocity and position functions were then obtained via successive numeric integrations\012\012    pos := proc( x )\012        local n;\012\012        if type( x, 'undefined' ) then\012            return x;\012        end if;\012\012        n := floor( 10*x );\012\012        return pospts[n,2] + ( pospts[n+1,2] - pospts[n,2] ) / ( pospts[n+1,1] - pospts[n,1] ) *\012                ( x - pospts[n,1] );\012    end proc; # pos_fn\012\012    vel := proc( x )\012        local n;\012\012        if type( x, 'undefined' ) then\012            return x;\012        end if;\012\012        n := floor( 10*x );\012\012        return velpts[n,2] + ( velpts[n+1,2] - velpts[n,2] ) / ( velpts[n+1,1] - velpts[n,1] ) *\012                ( x - velpts[n,1] );\012    end proc; # vel_fn\012\012    acc := proc( x )\012        local n;\012\012        if type( x, 'undefined' ) then\012            return x;\012        end if;\012\012        n := floor( 10*x );\012\012        return accpts[n,2] + ( accpts[n+1,2] - accpts[n,2] ) / ( accpts[n+1,1] - accpts[n,1] ) *\012                ( x - accpts[n,1] );\012    end proc; # acc_fn\012\012    jrk := proc( x )\012        local n;\012\012        if type( x, 'undefined' ) then\012            return x;\012        end if;\012\012        n := floor( 10*x );\012\012        return jrkpts[n,2] + ( jrkpts[n+1,2] - jrkpts[n,2] ) / ( jrkpts[n+1,1] - jrkpts[n,1] ) *\012                ( x - jrkpts[n,1] );\012    end proc; # jrk_fn\012\012    pospts := [[0., 0.], [.1, 28.92904596], [.2, 57.35410894], [.3, 85.27529860], [.4, 112.6927978], [.5, 139.6068628], [.6, 166.0178235], [.7, 191.9260836], [.8, 217.3321211], [.9, 242.2364887], [1.0, 266.6398142], [1.1, 290.5428011], [1.2, 313.9462293], [1.3, 336.8509557], [1.4, 359.2579147], [1.5, 381.1681196], [1.6, 402.5826629], [1.7, 423.5027175], [1.8, 443.9295376], [1.9, 463.8644600], [2.0, 483.3089049], [2.1, 502.2643773], [2.2, 520.7324682], [2.3, 538.7148560], [2.4, 556.2133077], [2.5, 573.2296806], [2.6, 589.7659237], [2.7, 605.8240791], [2.8, 621.4062842], [2.9, 636.5147726], [3.0, 651.1518767], [3.1, 665.3200289], [3.2, 679.0217639], [3.3, 692.2597206], [3.4, 705.0366439], [3.5, 717.3553871], [3.6, 729.2189139], [3.7, 740.6303007], [3.8, 751.5927389], [3.9, 762.1095371], [4.0, 772.1841239], [4.1, 781.8200498], [4.2, 791.0209903], [4.3, 799.7907483], [4.4, 808.1332567], [4.5, 816.0525814], [4.6, 823.5529239], [4.7, 830.6386240], [4.8, 837.3141634], [4.9, 843.5841677], [5.0, 849.4534106], [5.1, 854.9268162], [5.2, 860.0094624], [5.3, 864.7065839], [5.4, 869.0235747], [5.5, 872.9659902], [5.6, 876.5395486], [5.7, 879.7501326], [5.8, 882.6037894], [5.9, 885.1067315], [6.0, 887.2653363], [6.1, 889.0861452], [6.2, 890.5758628], [6.3, 891.7413553], [6.4, 892.5896480], [6.5, 893.1279232], [6.6, 893.3635173], [6.7, 893.3039170], [6.8, 892.9567554], [6.9, 892.3298082], [7.0, 891.4309882], [7.1, 890.2683404], [7.2, 888.8500363], [7.3, 887.1843672], [7.4, 885.2797385], [7.5, 883.1446614], [7.6, 880.7877463], [7.7, 878.2176943], [7.8, 875.4432888], [7.9, 872.4733865], [8.0, 869.3169078], [8.1, 865.9828276], [8.2, 862.4801642], [8.3, 858.8179696], [8.4, 855.0053196], [8.5, 851.0513039], [8.6, 846.9650176], [8.7, 842.7555522], [8.8, 838.4319880], [8.9, 834.0033855], [9.0, 829.4787792], [9.1, 824.8671699], [9.2, 820.1775188], [9.3, 815.4187414], [9.4, 810.5997022], [9.5, 805.7292092], [9.6, 800.8160097], [9.7, 795.8687861], [9.8, 790.8961519], [9.9, 785.9066485], [10.0, 780.9087426], [10.1, 775.9108235], [10.2, 770.9212012], [10.3, 765.9481049], [10.4, 760.9996818], [10.5, 756.0839968], [10.6, 751.2090318], [10.7, 746.3826862], [10.8, 741.6127777], [10.9, 736.9070432], [11.0, 732.2731403], [11.1, 727.7186495], [11.2, 723.2510767], [11.3, 718.8778556], [11.4, 714.6063515], [11.5, 710.4438652], [11.6, 706.3976364], [11.7, 702.4748491], [11.8, 698.6826366], [11.9, 695.0280865], [12.0, 691.5182473], [12.1, 688.1601344], [12.2, 684.9607369], [12.3, 681.9270243], [12.4, 679.0659525], [12.5, 676.3844692], [12.6, 673.8895184], [12.7, 671.5880451], [12.8, 669.4869980], [12.9, 667.5933326], [13.0, 665.9140132], [13.1, 664.4560143], [13.2, 663.2263214], [13.3, 662.2319310], [13.4, 661.4798499], [13.5, 660.9770941], [13.6, 660.7306869], [13.7, 660.7476561], [13.8, 661.0350310], [13.9, 661.5998383], [14.0, 662.4490974], [14.1, 663.5898155], [14.2, 665.0289814], [14.3, 666.7735605], [14.4, 668.8304894], [14.5, 671.2066725], [14.6, 673.9089790], [14.7, 676.9442408], [14.8, 680.3192518], [14.9, 684.0407682], [15.0, 688.1155087], [15.1, 692.5501574], [15.2, 697.3513661], [15.3, 702.5257586], [15.4, 708.0799353], [15.5, 714.0204793], [15.6, 720.3539631], [15.7, 727.0869563], [15.8, 734.2260347], [15.9, 741.7777897], [16.0, 749.7488392], [16.1, 758.1458390], [16.2, 766.9754960], [16.3, 776.2445811], [16.4, 785.9599443], [16.5, 796.1285302], [16.6, 806.7573943], [16.7, 817.8537205], [16.8, 829.4248399], [16.9, 841.4782499], [17.0, 854.0216347], [17.1, 867.0628865], [17.2, 880.6101271], [17.3, 894.6717245], [17.4, 909.2563036], [17.5, 924.3727465], [17.6, 940.0301856], [17.7, 956.2379871], [17.8, 973.0057265], [17.9, 990.3431546], [18.0, 1008.260156], [18.1, 1026.766698], [18.2, 1045.872772], [18.3, 1065.588334], [18.4, 1085.923246], [18.5, 1106.887215], [18.6, 1128.489750], [18.7, 1150.740102], [18.8, 1173.647227], [18.9, 1197.219735], [19.0, 1221.465857], [19.1, 1246.393403], [19.2, 1272.009731], [19.3, 1298.321717], [19.4, 1325.335726], [19.5, 1353.057591], [19.6, 1381.492590], [19.7, 1410.645428], [19.8, 1440.520223], [19.9, 1471.120499], [20.0, 1502.449171]];\012\012\012    velpts := [[0., 291.8105573], [.1, 286.7703620], [.2, 281.7308976], [.3, 276.6928955], [.4, 271.6570886], [.5, 266.6242116], [.6, 261.5950019], [.7, 256.5701999], [.8, 251.5505502], [.9, 246.5368016], [1.0, 241.5297083], [1.1, 236.5300303], [1.2, 231.5385340], [1.3, 226.5559929], [1.4, 221.5831882], [1.5, 216.6209096], [1.6, 211.6699559], [1.7, 206.7311355], [1.8, 201.8052672], [1.9, 196.8931806], [2.0, 191.9957172], [2.1, 187.1137306], [2.2, 182.2480875], [2.3, 177.3996679], [2.4, 172.5693663], [2.5, 167.7580919], [2.6, 162.9667695], [2.7, 158.1963399], [2.8, 153.4477610], [2.9, 148.7220078], [3.0, 144.0200737], [3.1, 139.3429706], [3.2, 134.6917300], [3.3, 130.0674033], [3.4, 125.4710626], [3.5, 120.9038013], [3.6, 116.3667349], [3.7, 111.8610014], [3.8, 107.3877622], [3.9, 102.9482024], [4.0, 98.5435319], [4.1, 94.1749856], [4.2, 89.8438243], [4.3, 85.5513355], [4.4, 81.2988336], [4.5, 77.0876609], [4.6, 72.9191881], [4.7, 68.7948150], [4.8, 64.7159711], [4.9, 60.6841164], [5.0, 56.7007418], [5.1, 52.7673698], [5.2, 48.88555416], [5.3, 45.05687612], [5.4, 41.28294015], [5.5, 37.56536920], [5.6, 33.90580014], [5.7, 30.30587917], [5.8, 26.76725718], [5.9, 23.29158519], [6.0, 19.88050975], [6.1, 16.53566829], [6.2, 13.25868459], [6.3, 10.05116413], [6.4, 6.91468950], [6.5, 3.85081582], [6.6, .86106611], [6.7, -2.05307328], [6.8, -4.89015730], [6.9, -7.64878678], [7.0, -10.32761301], [7.1, -12.92534241], [7.2, -15.44074105], [7.3, -17.87263929], [7.4, -20.21993640], [7.5, -22.48160511], [7.6, -24.65669623], [7.7, -26.74434328], [7.8, -28.74376705], [7.9, -30.65428021], [8.0, -32.47529193], [8.1, -34.20631238], [8.2, -35.84695533], [8.3, -37.39693572], [8.4, -38.85606538], [8.5, -40.22424860], [8.6, -41.50147772], [8.7, -42.68782872], [8.8, -43.78345680], [8.9, -44.78859200], [9.0, -45.70353478], [9.1, -46.52865159], [9.2, -47.26437050], [9.3, -47.91117675], [9.4, -48.46960838], [9.5, -48.94025177], [9.6, -49.32373731], [9.7, -49.62073490], [9.8, -49.83194962], [9.9, -49.95811728], [10., -50.], [10.1, -49.95838184], [10.2, -49.83406437], [10.3, -49.62786226], [10.4, -49.34059887], [10.5, -48.97310184], [10.6, -48.52619871], [10.7, -48.00071247], [10.8, -47.39745718], [10.9, -46.71723353], [11.0, -45.96082448], [11.1, -45.12899080], [11.2, -44.22246671], [11.3, -43.24195542], [11.4, -42.18812476], [11.5, -41.06160276], [11.6, -39.86297323], [11.7, -38.59277138], [11.8, -37.25147938], [11.9, -35.83952196], [12.0, -34.35726201], [12.1, -32.80499627], [12.2, -31.18295338], [12.3, -29.49129810], [12.4, -27.73013782], [12.5, -25.89952928], [12.6, -23.99948522], [12.7, -22.02998101], [12.8, -19.99096135], [12.9, -17.88234692], [13.0, -15.70404104], [13.1, -13.45593634], [13.2, -11.13792141], [13.3, -8.74988749], [13.4, -6.29173510], [13.5, -3.76338073], [13.6, -1.16476349], [13.7, 1.50414824], [13.8, 4.24335009], [13.9, 7.05279513], [14.0, 9.93238712], [14.1, 12.88197404], [14.2, 15.90134505], [14.3, 18.99023658], [14.4, 22.14834182], [14.5, 25.37532046], [14.6, 28.67080836], [14.7, 32.03442723], [14.8, 35.46579438], [14.9, 38.96453236], [15.0, 42.53027867], [15.1, 46.16269546], [15.2, 49.86147924], [15.3, 53.6263705], [15.4, 57.4571636], [15.5, 61.3537161], [15.6, 65.3159590], [15.7, 69.3439057], [15.8, 73.4376624], [15.9, 77.5974376], [16.0, 81.8235513], [16.1, 86.1164455], [16.2, 90.4766932], [16.3, 94.9050085], [16.4, 99.4022563], [16.5, 103.9694616], [16.6, 108.6078196], [16.7, 113.3187054], [16.8, 118.1036832], [16.9, 122.9645168], [17.0, 127.9031784], [17.1, 132.9218583], [17.2, 138.0229522], [17.3, 143.2089970], [17.4, 148.4825842], [17.5, 153.8462739], [17.6, 159.3025078], [17.7, 164.8535228], [17.8, 170.5012642], [17.9, 176.2472990], [18.0, 182.0927298], [18.1, 188.0381084], [18.2, 194.0833763], [18.3, 200.2278700], [18.4, 206.4703517], [18.5, 212.8090412], [18.6, 219.2416479], [18.7, 225.7654027], [18.8, 232.3770898], [18.9, 239.0730789], [19.0, 245.8493565], [19.1, 252.7015585], [19.2, 259.6250016], [19.3, 266.6147155], [19.4, 273.6654747], [19.5, 280.7718302], [19.6, 287.9281418], [19.7, 295.1286096], [19.8, 302.3673062], [19.9, 309.6382086], [20.0, 316.9352299]];\012\012\012    accpts := [[0., -50.40317089], [.1, -50.39951712], [.2, -50.38855259], [.3, -50.37026759], [.4, -50.34464597], [.5, -50.31166510], [.6, -50.27129591], [.7, -50.22350285], [.8, -50.16824390], [.9, -50.10547059], [1.0, -50.03512798], [1.1, -49.95715468], [1.2, -49.87148282], [1.3, -49.77803807], [1.4, -49.67673964], [1.5, -49.56750028], [1.6, -49.45022628], [1.7, -49.32481744], [1.8, -49.19116714], [1.9, -49.04916226], [2.0, -48.89868324], [2.1, -48.73960404], [2.2, -48.57179216], [2.3, -48.39510866], [2.4, -48.20940810], [2.5, -48.01453860], [2.6, -47.81034181], [2.7, -47.59665292], [2.8, -47.37330065], [2.9, -47.14010728], [3.0, -46.89688859], [3.1, -46.64345392], [3.2, -46.37960614], [3.3, -46.10514167], [3.4, -45.81985045], [3.5, -45.52351595], [3.6, -45.21591521], [3.7, -44.89681877], [3.8, -44.56599074], [3.9, -44.22318873], [4.0, -43.86816392], [4.1, -43.50066101], [4.2, -43.12041824], [4.3, -42.72716738], [4.4, -42.32063376], [4.5, -41.90053622], [4.6, -41.46658714], [4.7, -41.01849246], [4.8, -40.55595164], [4.9, -40.07865766], [5.0, -39.58629707], [5.1, -39.07855213], [5.2, -38.55512485], [5.3, -38.01576108], [5.4, -37.46025267], [5.5, -36.88843745], [5.6, -36.30019926], [5.7, -35.69546795], [5.8, -35.07421936], [5.9, -34.43647534], [6.0, -33.78230372], [6.1, -33.11181835], [6.2, -32.42517908], [6.3, -31.72259175], [6.4, -31.00430821], [6.5, -30.27062631], [6.6, -29.52188988], [6.7, -28.75848879], [6.8, -27.98085887], [6.9, -27.18948198], [7.0, -26.38488596], [7.1, -25.56764467], [7.2, -24.73837795], [7.3, -23.89775165], [7.4, -23.04647763], [7.5, -22.18531373], [7.6, -21.31506381], [7.7, -20.43657772], [7.8, -19.55075132], [7.9, -18.65852645], [8.0, -17.76089097], [8.1, -16.85887498], [8.2, -15.95350954], [8.3, -15.04578537], [8.4, -14.13664911], [8.5, -13.22700331], [8.6, -12.31770644], [8.7, -11.40957286], [8.8, -10.50337288], [8.9, -9.599832686], [9.0, -8.699634404], [9.1, -7.803416060], [9.2, -6.911771597], [9.3, -6.025250870], [9.4, -5.144359648], [9.5, -4.269559612], [9.6, -3.401268357], [9.7, -2.539859390], [9.8, -1.685662134], [9.9, -.8389619214], [10., 0.], [10.1, .8310264698], [10.2, 1.653964415], [10.3, 2.468704848], [10.4, 3.275182870], [10.5, 4.073377668], [10.6, 4.863312515], [10.7, 5.645054774], [10.8, 6.418715891], [10.9, 7.184451402], [11.0, 7.942460928], [11.1, 8.692988177], [11.2, 9.436320945], [11.3, 10.17279111], [11.4, 10.90277465], [11.5, 11.62669162], [11.6, 12.34500615], [11.7, 13.05822649], [11.8, 13.76690493], [11.9, 14.47163790], [12.0, 15.17306588], [12.1, 15.87186883], [12.2, 16.56871544], [12.3, 17.26421240], [12.4, 17.95889973], [12.5, 18.65325085], [12.6, 19.34767254], [12.7, 20.04250494], [12.8, 20.73802156], [12.9, 21.43442929], [13.0, 22.13186839], [13.1, 22.83041245], [13.2, 23.53006849], [13.3, 24.23077684], [13.4, 24.93241124], [13.5, 25.63477876], [13.6, 26.33761989], [13.7, 27.04060843], [13.8, 27.74335159], [13.9, 28.44538993], [14.0, 29.14619739], [14.1, 29.84518808], [14.2, 30.54179127], [14.3, 31.23552636], [14.4, 31.92600970], [14.5, 32.61295458], [14.6, 33.29617123], [14.7, 33.97556682], [14.8, 34.65114548], [14.9, 35.32300827], [15.0, 35.99135320], [15.1, 36.65647522], [15.2, 37.31876623], [15.3, 37.97871507], [15.4, 38.63690752], [15.5, 39.29402631], [15.6, 39.95085112], [15.7, 40.60825855], [15.8, 41.26722218], [15.9, 41.92881249], [16.0, 42.59419695], [16.1, 43.26463995], [16.2, 43.94150281], [16.3, 44.62624383], [16.4, 45.32041821], [16.5, 46.02567814], [16.6, 46.74377273], [16.7, 47.47654802], [16.8, 48.22594702], [16.9, 48.99400968], [17.0, 49.78287288], [17.1, 50.59473031], [17.2, 51.43139102], [17.3, 52.29383791], [17.4, 53.18218760], [17.5, 54.09569047], [17.6, 55.03273059], [17.7, 55.99082581], [17.8, 56.96662767], [17.9, 57.95592147], [18.0, 58.95362622], [18.1, 59.95384406], [18.2, 60.95040351], [18.3, 61.93740270], [18.4, 62.90925881], [18.5, 63.86070801], [18.6, 64.78680551], [18.7, 65.68292553], [18.8, 66.54476131], [18.9, 67.36832511], [19.0, 68.14994821], [19.1, 68.88628091], [19.2, 69.57429253], [19.3, 70.21127139], [19.4, 70.79482487], [19.5, 71.32287933], [19.6, 71.79368017], [19.7, 72.20579180], [19.8, 72.55809766], [19.9, 72.84980019], [20.0, 73.08042087]];\012\012\012    jrkpts := [[0., 0.], [.1, 0.7308075e-1], [.2, .14622614], [.3, .219500785], [.4, .292969330], [.5, .366696409], [.6, .440746643], [.7, .515184665], [.8, .590075116], [.9, .665482620], [1.0, .741471818], [1.1, .818107341], [1.2, .895453792], [1.3, .973575854], [1.4, 1.052538127], [1.5, 1.132405245], [1.6, 1.213241838], [1.7, 1.295112550], [1.8, 1.378082012], [1.9, 1.462214847], [2.0, 1.547575685], [2.1, 1.634229161], [2.2, 1.722239924], [2.3, 1.811672588], [2.4, 1.902591785], [2.5, 1.995062146], [2.6, 2.089148313], [2.7, 2.184914920], [2.8, 2.282426587], [2.9, 2.381747936], [3.0, 2.482943641], [3.1, 2.586078292], [3.2, 2.691216543], [3.3, 2.798423004], [3.4, 2.907762338], [3.5, 3.019299167], [3.6, 3.133098103], [3.7, 3.249223799], [3.8, 3.367740875], [3.9, 3.488713985], [4.0, 3.612207730], [4.1, 3.738286752], [4.2, 3.867015703], [4.3, 3.998459196], [4.4, 4.132681862], [4.5, 4.269748334], [4.6, 4.409723256], [4.7, 4.552671252], [4.8, 4.698656956], [4.9, 4.847744986], [5.0, 5.000000005], [5.1, 5.155399167], [5.2, 5.313569931], [5.3, 5.474052301], [5.4, 5.636386252], [5.5, 5.800111780], [5.6, 5.964768879], [5.7, 6.129897565], [5.8, 6.295037823], [5.9, 6.459729637], [6.0, 6.623513003], [6.1, 6.785927926], [6.2, 6.946514391], [6.3, 7.104812413], [6.4, 7.260361967], [6.5, 7.412703059], [6.6, 7.561375662], [6.7, 7.705919803], [6.8, 7.845875457], [6.9, 7.980782634], [7.0, 8.110181314], [7.1, 8.233611499], [7.2, 8.350613173], [7.3, 8.460726351], [7.4, 8.563491019], [7.5, 8.658447170], [7.6, 8.745134790], [7.7, 8.823093894], [7.8, 8.891864468], [7.9, 8.950986507], [8.0, 9.000000000], [8.1, 9.038595096], [8.2, 9.067062515], [8.3, 9.085843127], [8.4, 9.095377800], [8.5, 9.096107402], [8.6, 9.088472803], [8.7, 9.072914871], [8.8, 9.049874477], [8.9, 9.019792487], [9.0, 8.983109771], [9.1, 8.940267198], [9.2, 8.891705635], [9.3, 8.837865954], [9.4, 8.779189023], [9.5, 8.716115708], [9.6, 8.649086881], [9.7, 8.578543409], [9.8, 8.504926163], [9.9, 8.428676008], [10., 8.350233817], [10.1, 8.270040456], [10.2, 8.188536795], [10.3, 8.106163703], [10.4, 8.023362047], [10.5, 7.940572698], [10.6, 7.858236523], [10.7, 7.776794394], [10.8, 7.696687177], [10.9, 7.618355740], [11.0, 7.542240955], [11.1, 7.468783687], [11.2, 7.398424809], [11.3, 7.331605187], [11.4, 7.268765689], [11.5, 7.210347188], [11.6, 7.156790548], [11.7, 7.108536641], [11.8, 7.066026335], [11.9, 7.029700498], [12.0, 7.000000000], [12.1, 6.977181177], [12.2, 6.960762244], [12.3, 6.950076882], [12.4, 6.944458774], [12.5, 6.943241601], [12.6, 6.945759044], [12.7, 6.951344787], [12.8, 6.959332513], [12.9, 6.969055900], [13.0, 6.979848634], [13.1, 6.991044398], [13.2, 7.001976862], [13.3, 7.011979729], [13.4, 7.020386663], [13.5, 7.026531345], [13.6, 7.029747477], [13.7, 7.029368721], [13.8, 7.024728760], [13.9, 7.015161305], [14.0, 6.99999999], [14.1, 6.97885118], [14.2, 6.95241163], [14.3, 6.92165081], [14.4, 6.88753816], [14.5, 6.85104312], [14.6, 6.81313513], [14.7, 6.77478361], [14.8, 6.73695803], [14.9, 6.70062780], [15.0, 6.66676239], [15.1, 6.63633120], [15.2, 6.61030372], [15.3, 6.58964935], [15.4, 6.57533754], [15.5, 6.56833775], [15.6, 6.56961939], [15.7, 6.58015192], [15.8, 6.60090475], [15.9, 6.63284735], [16.0, 6.67694916], [16.1, 6.73417960], [16.2, 6.80550814], [16.3, 6.89190419], [16.4, 6.99433719], [16.5, 7.11377660], [16.6, 7.25119184], [16.7, 7.40755232], [16.8, 7.58382764], [16.9, 7.78098696], [17.0, 7.9999996], [17.1, 8.2402309], [17.2, 8.4946225], [17.3, 8.7545095], [17.4, 9.0112333], [17.5, 9.2561303], [17.6, 9.4805366], [17.7, 9.6757867], [17.8, 9.8332239], [17.9, 9.9441824], [18.0, 10.0000001], [18.1, 9.9939888], [18.2, 9.9273641], [18.3, 9.8033161], [18.4, 9.6250340], [18.5, 9.3957090], [18.6, 9.1185314], [18.7, 8.7966913], [18.8, 8.4333789], [18.9, 8.0317834], [19.0, 7.5950969], [19.1, 7.1265068], [19.2, 6.6292061], [19.3, 6.1063841], [19.4, 5.5612299], [19.5, 4.9969358], [19.6, 4.4166891], [19.7, 3.8236826], [19.8, 3.2211058], [19.9, 2.6121477], [20.0, 2.0000007]];\012\012\012    plts := ['Plot5', 'Plot6', 'Plot7', 'Plot8'];\012    fns := [pos, vel, acc, jrk];\012    ttls := [&quot;Posi\303\247\303\243o&quot;, &quot;Velocidade&quot;, &quot;Acelera\303\247\303\243o&quot;, &quot;Arrancada&quot;];\012    pts := [pospts, velpts, accpts, jrkpts];\012\012    view0 := [[0..20, 0..1550], [0..20, -100..350], [0..20, -50..80], [0..20, 0..10]];\012\012    Init := proc( pt );\012        x := pt;\012        DoPlot();\012    end proc; # Init\012\012    Click := proc( plt )\012        x := DT:-GetProperty( plt, &quot;clickx&quot; );\012        DoPlot();\012    end proc; # Click\012\012    Drag := proc( plt )\012        x := DT:-GetProperty( plt, &quot;endx&quot; );\012        DoPlot();\012    end proc; # Drag\012\012    DoPlot := proc()\012        local i;\012\012        for i from 1 to 4 do\012            DT:-SetProperty( plts[i], value, plots:-display( [\012                    plots:-pointplot( pts[i], 'style' = 'line' ),\012                    plots:-pointplot( \012                        [[x, lhs( view0[i][2] )], [x, rhs( view0[i][2] )]],\012                        'style' = 'line',\012                        'colour' = 'grey' ),\012                    plots:-pointplot( \012                        [x, fns[i]( x )],\012                        'style' = 'point',\012                        'colour' = 'red',\012                        'symbol' = 'solidcircle',\012                        'symbolsize' = 20 )\012                ],\012                'title' = ttls[i],\012                'labels' = ['t', 'y'],\012                'axis'[2] = ['tickmarks' = 0] )\012                );\012        end do;\012    end proc; # DoPlot\012\012end module; # M4_2_3b\012\012\012# Initialize components\012proc()\012    local PosData, SpdData;\012    uses DT = DocumentTools;\012\012    PosData := Matrix( [[0., 0.], [.105, 0.153e-4], [.197, 0.187e-3], [.300, 0.101e-2], [.403, 0.330e-2], [.506, 0.821e-2], [.602, 0.164e-1], [.701, 0.301e-1], [.803, 0.520e-1], [.905, 0.839e-1], [1.01, .130], [1.10, .185], [1.21, .264], [1.31, .366], [1.41, .487], [1.50, .617], [1.61, .797], [1.70, .972], [1.81, 1.20], [1.91, 1.42], [2.01, 1.69], [2.11, 1.97], [2.21, 2.27], [2.31, 2.57], [2.41, 2.91], [2.52, 3.27], [2.61, 3.59], [2.71, 3.95], [2.81, 4.33], [2.91, 4.71], [3.01, 5.08], [3.12, 5.50], [3.22, 5.88], [3.32, 6.29], [3.42, 6.67], [3.52, 7.08], [3.62, 7.46], [3.72, 7.87], [3.82, 8.27], [3.92, 8.68], [4.02, 9.08], [4.12, 9.49], [4.22, 9.90], [4.32, 10.3], [4.42, 10.7], [4.52, 11.1], [4.62, 11.5], [4.72, 11.9], [4.83, 12.3], [4.92, 12.7], [5.03, 13.1], [5.12, 13.5], [5.23, 13.9], [5.32, 14.3], [5.43, 14.7], [5.53, 15.1], [5.63, 15.5], [5.73, 15.9], [5.82, 16.3], [5.93, 16.7], [6.03, 17.1], [6.13, 17.5], [6.23, 17.9], [6.33, 18.3], [6.43, 18.7], [6.53, 19.1], [6.64, 19.5], [6.73, 19.9], [6.83, 20.3], [6.94, 20.7], [7.04, 21.1], [7.14, 21.4], [7.24, 21.8], [7.33, 22.1], [7.43, 22.4], [7.53, 22.7], [7.64, 23.0], [7.73, 23.2], [7.84, 23.5], [7.94, 23.7], [8.04, 24.0], [8.14, 24.2], [8.25, 24.4], [8.34, 24.5], [8.44, 24.7], [8.54, 24.9], [8.65, 25.0], [8.74, 25.1], [8.85, 25.3], [8.95, 25.4], [9.04, 25.5], [9.14, 25.6], [9.24, 25.7], [9.35, 25.8], [9.45, 25.9], [9.55, 26.0], [9.65, 26.1], [9.75, 26.3], [9.84, 26.3], [9.95, 26.5], [10.0, 26.5], [10.2, 26.7], [10.3, 26.8], [10.3, 26.8], [10.5, 27.0], [10.6, 27.1], [10.7, 27.2], [10.8, 27.3], [10.9, 27.4], [11.0, 27.5], [11.1, 27.6], [11.2, 27.7], [11.3, 27.8], [11.4, 27.9], [11.5, 28.0], [11.6, 28.1], [11.7, 28.2], [11.8, 28.3], [11.9, 28.4], [12.0, 28.5], [12.1, 28.6], [12.2, 28.7], [12.3, 28.8], [12.4, 28.9], [12.5, 29.0], [12.6, 29.1], [12.7, 29.2], [12.8, 29.3], [12.9, 29.4], [13.0, 29.5], [13.1, 29.6], [13.2, 29.7], [13.3, 29.9], [13.4, 30.0], [13.5, 30.2], [13.6, 30.3], [13.7, 30.5], [13.8, 30.6], [13.9, 30.8], [14.0, 31.0], [14.1, 31.2], [14.2, 31.4], [14.3, 31.6], [14.4, 31.8], [14.5, 32.0], [14.6, 32.2], [14.7, 32.4], [14.8, 32.6], [14.9, 32.8], [15.0, 33.1], [15.1, 33.3], [15.2, 33.5], [15.3, 33.7], [15.4, 33.9], [15.5, 34.1], [15.6, 34.3], [15.7, 34.5], [15.8, 34.7], [15.9, 34.9], [16.0, 35.1], [16.1, 35.3], [16.2, 35.5], [16.3, 35.7], [16.4, 35.8], [16.5, 36.0], [16.6, 36.1], [16.7, 36.3], [16.8, 36.4], [16.9, 36.5], [17.0, 36.6], [17.1, 36.8], [17.2, 36.9], [17.3, 37.0], [17.4, 37.1], [17.5, 37.2], [17.6, 37.3], [17.7, 37.4], [17.8, 37.5], [17.9, 37.6], [18.0, 37.7], [18.1, 37.7], [18.2, 37.8], [18.3, 37.9], [18.4, 37.9], [18.5, 38.0], [18.6, 38.0], [18.7, 38.1], [18.8, 38.1], [18.9, 38.1], [19.0, 38.2], [19.1, 38.2], [19.2, 38.2], [19.3, 38.2], [19.4, 38.2], [19.5, 38.2], [19.6, 38.2], [19.7, 38.2], [19.8, 38.2], [19.9, 38.2], [20., 38.2]] );\012\012    SpdData := Matrix( [[0., 0.], [.105, 0.581e-3], [.197, 0.380e-2], [.300, 0.134e-1], [.403, 0.328e-1], [.506, 0.649e-1], [.602, .109], [.701, .172], [.803, .259], [.905, .371], [1.01, .515], [1.10, .669], [1.21, .866], [1.31, 1.09], [1.41, 1.31], [1.50, 1.53], [1.61, 1.79], [1.70, 2.01], [1.81, 2.26], [1.91, 2.47], [2.01, 2.69], [2.11, 2.87], [2.21, 3.05], [2.31, 3.19], [2.41, 3.33], [2.52, 3.46], [2.61, 3.55], [2.71, 3.64], [2.81, 3.72], [2.91, 3.79], [3.01, 3.84], [3.12, 3.89], [3.22, 3.92], [3.32, 3.95], [3.42, 3.97], [3.52, 3.98], [3.62, 3.99], [3.72, 4.00], [3.82, 4.00], [3.92, 4.00], [4.02, 4.], [4.12, 4.], [4.22, 4.], [4.32, 4.], [4.42, 4.], [4.52, 4.], [4.62, 4.], [4.72, 4.], [4.83, 4.], [4.92, 4.], [5.03, 4.], [5.12, 4.], [5.23, 4.], [5.32, 4.], [5.43, 4.], [5.53, 4.], [5.63, 4.], [5.73, 4.], [5.82, 4.], [5.93, 4.], [6.03, 4.00], [6.13, 4.00], [6.23, 4.00], [6.33, 3.99], [6.43, 3.97], [6.53, 3.95], [6.64, 3.91], [6.73, 3.87], [6.83, 3.81], [6.94, 3.72], [7.04, 3.63], [7.14, 3.51], [7.24, 3.38], [7.33, 3.24], [7.43, 3.08], [7.53, 2.92], [7.64, 2.75], [7.73, 2.59], [7.84, 2.41], [7.94, 2.26], [8.04, 2.11], [8.14, 1.96], [8.25, 1.83], [8.34, 1.71], [8.44, 1.60], [8.54, 1.50], [8.65, 1.41], [8.74, 1.33], [8.85, 1.26], [8.95, 1.20], [9.04, 1.15], [9.14, 1.10], [9.24, 1.07], [9.35, 1.05], [9.45, 1.03], [9.55, 1.02], [9.65, 1.01], [9.75, 1.00], [9.84, 1.00], [9.95, 1.00], [10.0, 1.], [10.2, 1.], [10.3, 1.], [10.3, 1.], [10.5, 1.], [10.6, 1.], [10.7, 1.], [10.8, 1.], [10.9, 1.], [11.0, 1.], [11.1, 1.], [11.2, 1.], [11.3, 1.], [11.4, 1.], [11.5, 1.], [11.6, 1.], [11.7, 1.], [11.8, 1.], [11.9, 1.], [12.0, 1.], [12.1, 1.00], [12.2, 1.00], [12.3, 1.00], [12.4, 1.01], [12.5, 1.02], [12.6, 1.03], [12.7, 1.05], [12.8, 1.07], [12.9, 1.11], [13.0, 1.15], [13.1, 1.20], [13.2, 1.26], [13.3, 1.33], [13.4, 1.40], [13.5, 1.48], [13.6, 1.56], [13.7, 1.64], [13.8, 1.71], [13.9, 1.78], [14.0, 1.85], [14.1, 1.91], [14.2, 1.96], [14.3, 2.00], [14.4, 2.04], [14.5, 2.07], [14.6, 2.09], [14.7, 2.11], [14.8, 2.12], [14.9, 2.13], [15.0, 2.13], [15.1, 2.13], [15.2, 2.13], [15.3, 2.12], [15.4, 2.10], [15.5, 2.08], [15.6, 2.05], [15.7, 2.02], [15.8, 1.98], [15.9, 1.93], [16.0, 1.88], [16.1, 1.82], [16.2, 1.75], [16.3, 1.67], [16.4, 1.60], [16.5, 1.52], [16.6, 1.44], [16.7, 1.37], [16.8, 1.29], [16.9, 1.23], [17.0, 1.18], [17.1, 1.13], [17.2, 1.09], [17.3, 1.06], [17.4, 1.03], [17.5, 1.00], [17.6, .978], [17.7, .952], [17.8, .919], [17.9, .885], [18.0, .836], [18.1, .784], [18.2, .724], [18.3, .653], [18.4, .577], [18.5, .506], [18.6, .431], [18.7, .359], [18.8, .285], [18.9, .227], [19.0, .169], [19.1, .123], [19.2, 0.870e-1], [19.3, 0.587e-1], [19.4, 0.370e-1], [19.5, 0.207e-1], [19.6, 0.107e-1], [19.7, 0.468e-2], [19.8, 0.134e-2], [19.9, 0.153e-3], [20., 0.]] );\012\012    PosPlot := plots:-pointplot( PosData, 'colour' = 'red', 'style' = 'line' );\012    SpdPlot := plots:-pointplot( SpdData, 'colour' = 'blue', 'style' = 'line' );\012\012    DT:-Do( %Plot0 = plots:-display( SpdPlot, 'view' = [0..20, 0..5],\012            'labels' = [&quot;Tempo&quot;, &quot;Velocidade&quot;], 'labeldirections' = ['horizontal', 'vertical'],\012            'tickmarks' = [5, [0 = 0, 1 = 10, 2 = 20, 3 = 30, 4 = 40, 5 = 50]] ) );\012    DT:-Do( %Plot1 = plots:-display( PosPlot, 'view' = [0..20, 0..40],\012            'labels' = [&quot;Tempo&quot;, &quot;Dist\303\242ncia&quot;], 'labeldirections' = ['horizontal', 'vertical'],\012            'tickmarks' = [5, [0 = 0, 20 = 5, 40 = 10]] ) );\012    DT:-Do( %Plot2 = plots:-display( [ PosPlot,\012            plots:-pointplot( [[0, 0], [20, 38.2]], 'style' = 'line', 'colour' = 'magenta' ),\012            plots:-textplot( [10, 17, &quot;r ~ .5&quot;], 'align' = ['below', 'right'], 'colour' = 'magenta' ) ],\012            'view' = [0..20, 0..40],\012            'labels' = [&quot;Tempo&quot;, &quot;Dist\303\242ncia&quot;], 'labeldirections' = ['horizontal', 'vertical'],\012            'tickmarks' = [5, [0 = 0, 20 = 5, 40 = 10]] ) );\012\012    M4_2_3b:-Init( 5.0 );\012end proc();\012"/>
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<Input><Text-field style="Text" layout="Normal" alignment="centred"><Font size="18" bold="true" encoding="UTF-8">Fun\303\247\303\243o do Primeiro Grau:</Font></Text-field>
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<Input><Text-field style="Text" layout="Normal" alignment="centred"><Font size="18" bold="true" encoding="UTF-8">Taxa M\303\251dia de Varia\303\247\303\243o</Font></Text-field>
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<Input><Text-field style="Text" layout="Normal"><Font encoding="UTF-8">Conhecer a localiza\303\247\303\243o de algo, como um foguete, muitas vezes n\303\243o \303\251 t\303\243o importante como saber sua </Font><Font italic="true">velocidade</Font><Font encoding="UTF-8">\342\200\224qu\303\243o r\303\241pido ele vai .Saber a sua velocidade muitas vezes n\303\243o \303\251 t\303\243o importante quanto saber sua <Font italic="true">acelera\303\247\303\243o</Font>\342\200\224a rapidez com que est\303\241 acelerando ou retardando. E, se voc\303\252 est\303\241 no neg\303\263cio de (com seguran\303\247a) pessoas saltando malucas ao redor de um parque de divers\303\243o, sabendo que a acelera\303\247\303\243o n\303\243o pode ser t\303\243o importante quanto saber o empurr\303\243o\342\200\224a rapidez com que a acelera\303\247\303\243o est\303\241 mudando, porque o corpo humano s\303\263 pode suportar tanta excita\303\247\303\243o. </Font></Text-field>
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<Input><Text-field style="Text" layout="Title" alignment="left"><Font encoding="UTF-8">Nesta apresenta\303\247\303\243o, iremos introduzir os conceitos de <Font italic="true">taxa de varia\303\247\303\243o m\303\251dia, acelera\303\247\303\243o e velocidade.</Font></Font></Text-field>
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<Input><Text-field style="Text" layout="Title" alignment="left"><Font encoding="UTF-8">Vamos supor que voc\303\252 esteja familiarizado com esses conceitos complementares, que s\303\243o apresentadas em outra parte nesta cole\303\247\303\243o:<Font italic="true"> inclina\303\247\303\243o, dom\303\255nio, fun\303\247\303\243o, reta secante e  valor absoluto.</Font></Font></Text-field>
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<Input><Text-field style="Text" layout="Normal"><Font encoding="UTF-8">Voc\303\252 pode estar familiarizado com a f\303\263rmula </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUkjbWlHRiQ2JlEvZGlzdCYjMjI2O25jaWFGJy8lJ2l0YWxpY0dRJXRydWVGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi5RIj1GJ0YyL0Y2USdub3JtYWxGJy8lJmZlbmNlR0Y0LyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRk4tRiw2JlErdmVsb2NpZGFkZUYnRi9GMkY1LUY5Ni5RKCZ0aW1lcztGJ0YyRjxGPkZARkJGREZGRkhGSi9GTVEsMC4yMjIyMjIyZW1GJy9GUEZYLUYsNiZRJnRlbXBvRidGL0YyRjVGMkY8">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</Equation><Font encoding="UTF-8">. Para um objeto, tal como o seu carro, viajando a uma velocidade constante, esta f\303\263rmula d\303\241-lhe uma maneira de calcular o quanto voc\303\252 viajou, se voc\303\252 sabe o qu\303\243o r\303\241pido voc\303\252 estava indo e quanto tempo voc\303\252 estava viajando. Reescrevendo isso, tamb\303\251m temos </Font><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation><Font encoding="UTF-8">, que lhe diz o qu\303\243o r\303\241pido voc\303\252 fosseise voc\303\252 sabe o quanto voc\303\252 foi e quanto tempo  voc\303\252 levou. \303\211 por isso que, por exemplo, as velocidades s\303\243o medidas em unidades como </Font><Font italic="true">milhas/hora</Font><Font encoding="UTF-8">, uma unidade de dist\303\242ncia (milhas), dividida por uma unidade de tempo (horas).</Font></Text-field>
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<Input><Text-field style="Text" layout="Normal"><Font encoding="UTF-8">Observe, entretanto, que \303\251 muito improv\303\241vel que voc\303\252 viaje na mesma velocidade durante todo o tempo. Voc\303\252 teria passado algum per\303\255odo de tempo acelerando, ent\303\243o algum tempo viajando a uma velocidade constante, ent\303\243o talvez voc\303\252 desaceleraria, aceleraria novamente e finalmente diminuiria para um ponto em seu destino. Assim, o gr\303\241fico da sua velocidade em <Font italic="true">fun\303\247\303\243o do tempo</Font></Font> poderia ser algo como isto:</Text-field>
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<Input><Text-field style="Text" layout="Normal"><Font encoding="UTF-8">As partes mais \303\255ngremes do gr\303\241fico correspondem aos momentos em que voc\303\252 estava indo mais r\303\241pido (como se estivesse cobrindo uma dist\303\242ncia maior em um determinado per\303\255odo de tempo), e as partes menos \303\255ngreme correspondem aos momentos em que voc\303\252 estava indo mais devagar. A f\303\263rmula </Font><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation><Font encoding="UTF-8"> suaviza as varia\303\247\303\265es encontradas, dando-lhe um \303\272nico n\303\272mero, que representa a velocidade m\303\251dia percorrida para chegar ao seu destino no tempo determinado.</Font></Text-field>
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<Input><Text-field style="Text" layout="Normal">A<Font bold="true" encoding="UTF-8"> taxa de varia\303\247\303\243o m\303\251dia</Font><Font encoding="UTF-8"> de uma fun\303\247\303\243o </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2JS1GLDYmUSJmRicvJSdpdGFsaWNHUSV0cnVlRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRidGNy9GO1Enbm9ybWFsRidGK0Y3Rj0=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2JS1GLDYmUSJmRicvJSdpdGFsaWNHUSV0cnVlRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRidGNy9GO1Enbm9ybWFsRidGK0Y3Rj0=</Equation> em um intervalo <Equation executable="false" style="2D Math" input-equation="" 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encoding="UTF-8">em seu dom\303\255nio \303\251 dado pela f\303\263rmula  </Font><Equation executable="false" style="2D Math" input-equation="" 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<Input><Text-field style="Text" layout="Normal"><Font encoding="UTF-8">Para o exemplo da sua posi\303\247\303\243o versus o tempo do gr\303\241fico apresentado acima, a velocidade m\303\251dia \303\251 a inclina\303\247\303\243o da reta que conecta as suas posi\303\247\303\265es iniciais e finais, mostrado em magenta aqui. Se a dist\303\242ncia \303\251 medida em milhas e tempo em minutos, ent\303\243o essa inclina\303\247\303\243o corresponde a cerca de 30 milhas / hora.</Font></Text-field>
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<Input><Text-field style="Text" layout="Normal"><Font encoding="UTF-8">Observe que a fun\303\247\303\243o deve ser definida nos extremos </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEiYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEiYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn</Equation> e <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEiYkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEiYkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn</Equation><Font encoding="UTF-8"> do intervalo, e que o intervalo \303\251 no dom\303\255nio de </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn</Equation>, de modo que <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn</Equation><Font encoding="UTF-8"> \303\251 definida em todos os pontos no intervalo.</Font></Text-field>
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<Input><Text-field style="Text" layout="Normal"><Font encoding="UTF-8">Note tamb\303\251m que ele deve ser o caso que </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JlEiYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LlErJk5vdEVxdWFsO0YnRjIvRjZRJ25vcm1hbEYnLyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTi1GLDYmUSJiRidGL0YyRjVGMkY8">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JlEiYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LlErJk5vdEVxdWFsO0YnRjIvRjZRJ25vcm1hbEYnLyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTi1GLDYmUSJiRidGL0YyRjVGMkY8</Equation><Font encoding="UTF-8">. No entanto, n\303\243o \303\251 necess\303\241rio que </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JlEiYkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LlEiPkYnRjIvRjZRJ25vcm1hbEYnLyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTi1GLDYmUSJhRidGL0YyRjVGMkY8">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JlEiYkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LlEiPkYnRjIvRjZRJ25vcm1hbEYnLyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTi1GLDYmUSJhRidGL0YyRjVGMkY8</Equation><Font encoding="UTF-8">. A f\303\263rmula ainda \303\251 v\303\241lida se </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JlEiYkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LlEiPEYnRjIvRjZRJ25vcm1hbEYnLyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTi1GLDYmUSJhRidGL0YyRjVGMkY8">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JlEiYkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LlEiPEYnRjIvRjZRJ25vcm1hbEYnLyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTi1GLDYmUSJhRidGL0YyRjVGMkY8</Equation>.</Text-field>
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<Input><Text-field style="Text" layout="Normal"><Font encoding="UTF-8">Finalmente, enquanto a express\303\243o<Font italic="true"> taxa de varia\303\247\303\243o</Font> sugere que a vari\303\241vel independente \303\251 o tempo, esse c\303\241lculo pode ser realizado por qualquer fun\303\247\303\243o, n\303\243o importa o que a vari\303\241vel independente representa. Se a vari\303\241vel independente representa algo diferente de tempo, \303\251 comum referir-se ao resultado de c\303\241lculo como a <Font italic="true">varia\303\247\303\243o m\303\251dia</Font> da fun\303\247\303\243o no intervalo </Font><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation>.</Text-field>
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<Section collapsed="true" isCollapsible="true" drawButton="true" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title><Text-field style="Heading 2" layout="Heading 2"><Font encoding="UTF-8">Terminologia: Acelera\303\247\303\243o e Velocidade</Font></Text-field></Title><Presentation-Block>
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<Input><Text-field style="Text" layout="Normal"><Font encoding="UTF-8">Muitas vezes voc\303\252 est\303\241 interessado apenas em qu\303\243o r\303\241pido algo se move. Em tais casos, \303\251 normal falar sobre a <Font bold="true">acelera\303\247\303\243o</Font></Font><Font bold="true"> </Font>do objeto<Font encoding="UTF-8">. Isto \303\251 o que o veloc\303\255metro de um autom\303\263vel mede.</Font></Text-field>
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<Input><Text-field style="Text" layout="Normal"><Font encoding="UTF-8">No entanto, n\303\243o \303\251 incomum que voc\303\252 precisa saber mais do que apenas a velocidade de um objeto, voc\303\252 tamb\303\251m precisa saber se ele est\303\241 se movendo para frente ou para tr\303\241s. Ou seja, voc\303\252 precisa saber n\303\243o s\303\263 como r\303\241pido, mas em qual dire\303\247\303\243o o objeto est\303\241 se movendo. Essas duas informa\303\247\303\265es s\303\243o combinadas em que \303\251 normalmente chamado de</Font><Font bold="true"> velocidade</Font><Font encoding="UTF-8"> do objeto: Para o movimento ao longo de uma pista reta, velocidade positiva significa que o objeto est\303\241 se afastando do seu ponto de partida, enquanto a velocidade negativa significa que o objeto est\303\241 se movendo em dire\303\247\303\243o ao seu ponto de partida. A rapidez \303\251 ent\303\243o o valor absoluto da velocidade.</Font></Text-field>
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<Input><Text-field style="Text" layout="Normal">No restante desta planilha, vamos usar a <Font italic="true">velocidade</Font> como o termo relacionado ao movimento de um objeto.</Text-field>
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<Input><Text-field style="Text" layout="Normal"><Font encoding="UTF-8">As duas parcelas abaixo ilustram bem como a taxa de varia\303\247\303\243o m\303\251dia de uma fun\303\247\303\243o de posi\303\247\303\243o se aproxima da fun\303\247\303\243o de velocidade correspondente (supondo que o movimento \303\251 ao longo de uma linha reta, para manter as coisas gerenci\303\241veis).</Font></Text-field>
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<Input><Text-field style="Text" layout="Normal"><Font encoding="UTF-8">Clique e arraste o gr\303\241fico de Posi\303\247\303\243o e veja as informa\303\247\303\265es resultantes mostrados nos gr\303\241ficos da Posi\303\247\303\243o e Velocidade.</Font></Text-field>
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<Input><Text-field style="Text" layout="Normal"><Font encoding="UTF-8">No gr\303\241fico Posi\303\247\303\243o, o ponto vermelho representa um valor de posi\303\247\303\243o. Os pontos verdes, situado a alguma dist\303\242ncia do ponto vermelho, representam momentos em que medidas de posi\303\247\303\243o t\303\252m sido tomadas. O declive da secante que liga os pontos verdes (a linha de cor magenta) \303\251 a taxa de varia\303\247\303\243o m\303\251dia da fun\303\247\303\243o de posi\303\247\303\243o ao longo deste intervalo de tempo. Esse valor \303\251 mostrado como o ponto vermelho no gr\303\241fico de velocidade. As retas verticais cinza sobre os dois gr\303\241ficos apenas indicam o mesmo valor de tempo em cada gr\303\241fico.</Font></Text-field>
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<Input><Text-field style="Text" layout="Normal"><Font encoding="UTF-8">Conforme voc\303\252 arrasta para a direita no gr\303\241fico posi\303\247\303\243o, a dist\303\242ncia entre os pontos verdes ir\303\241 aumentar. Quando voc\303\252 arrasta para a esquerda, essa dist\303\242ncia vai diminuir. Qu\303\243o bem a taxa de varia\303\247\303\243o m\303\251dia se aproxima da velocidade real?</Font></Text-field>
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<Input><Text-field style="Text" layout="Normal"><Font encoding="UTF-8">Clique para limpar o gr\303\241fico.</Font></Text-field>
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<Input><Text-field style="Text" layout="Normal"><Font encoding="UTF-8">Estes quatro gr\303\241ficos est\303\243o relacionados das seguintes maneiras:</Font></Text-field>
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<Input><Text-field style="Text" layout="Normal" bullet="dot"><Font encoding="UTF-8">Quando a velocidade \303\251 positiva, a posi\303\247\303\243o (dist\303\242ncia entre o local de partida) est\303\241 aumentando, e quando a velocidade for negativa, a posi\303\247\303\243o est\303\241 diminuindo.</Font></Text-field>
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